Digital EE141 Integrated Circuits 2nd Combinational Circuits


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1 Digital Integrated Circuits Designing i Combinational Logic Circuits 1
2 Combinational vs. Sequential Logic 2
3 Static CMOS Circuit t every point in time (except during the switching transients) each gate output is connected to either V DD or V ss via a lowresistive path. The outputs of the gates assume at all times the value of the oolean function, implemented by the circuit (ignoring, once again, the transient effects during switching periods). This is in contrast to the dynamic circuit class, which relies on temporary storage of signal values on the capacitance of high impedance circuit nodes. 3
4 Static Complementary CMOS V DD In1 In2 InN In1 In2 InN PUN PDN PMOS only F(In1,In2, InN), NMOS only PUN (pullup network) and PDN (pulldown network) are dual logic networks 4
5 NMOS Transistors in Series/Parallel l Connection Transistors can be thought as a switch controlled by its gate signal NMOS switch closes when switch control input is high X Y Y = X if and X Y Y = X if OR NMOS Transistors pass a strong 0buta weak 1 5
6 PMOS Transistors in Series/Parallel l Connection PMOS switch closes when switch control input is low X Y Y = X if ND = + X Y Y = X if OR = PMOS Transistors pass a strong 1 but a weak 0 6
7 Threshold Drops PUN V DD S V DD D V DD D 0 V S DD 0 V DD V Tn V GS C L C L PDN V DD 0 V DD V Tp VDD D C L V GS S C L S D 7
8 Complementary CMOS Logic Style 8
9 Example Gate: NND 9
10 Example Gate: NOR 10
11 Complex CMOS Gate C D D C OUT = D + ( + C) 11
12 Constructing a Complex Gate 12
13 Cell Design Standard Cells General purpose logic Can be synthesized Same height, varying width Datapath Cells For regular, structured designs (arithmetic) Includes some wiring in the cell Fixed height and width 13
14 Standard Cell Layout Methodology 1980s Routing channel V DD signals GND 14
15 Standard Cell Layout Methodology 1990s Mirrored Cell No Routing channels V DD V DD M2 M3 GND Mirrored Cell GND 15
16 Standard Cells N Well V DD Cell height ht 12 metal tracks Metal track is approx. 3λ + 3λ Pitch = repetitive distance between objects Cell height is 12 pitch 2λ In Out Cell boundary GND Rails ~10λ 16
17 Standard Cells With minimal diffusion routing V DD With silicided diffusion V DD V DD In M 2 Out In Out In Out M 1 GND GND 17
18 Standard Cells V DD 2input NND gate V DD Out GND 18
19 Stick Diagrams Contains no dimensions Represents relative positions of transistors Inverter V DD NND2 V DD Out Out GND In GND 19
20 Stick Diagrams j C Logic Graph X C PUN X = C (+ ) X i V DD C i j C GND PDN 20
21 Two Versions of C ( + ) C C V DD V DD X X GND GND 21
22 Consistent Euler Path X C X i V DD j GND C 22
23 OI22 Logic Graph C X PUN D D C X = (+) (C+D) X V DD C D C D GND PDN 23
24 Example: x = ab+cd x x b c b c x V DD x V DD a d a d GND GND (a) Logic graphs for (ab+cd) (b) Euler Paths {a b c d} V DD x GND a b c d (c) stick diagram for ordering {a b c d} 24
25 MultiFingered Transistors One finger Two fingers (folded) Less diffusion capacitance 25
26 Properties of Complementary CMOS Gates Snapshot High noise margins: V OH and V OL are at V DD and GND, respectively. No static power consumption: There never exists a direct path between V DD and V SS (GND)insteadystate state mode. Comparable rise and fall times: (under appropriate sizing conditions) 26
27 CMOS Properties Full railtorail swing; high noise margins Logic levels not dependent upon the relative device sizes; ratioless lways a path to Vdd or Gnd in steady state; low output impedance Extremely high input resistance; nearly zero steadystate state input current No direct path steady state between power and ground; no static power dissipation Propagation delay function of load capacitance and resistance of transistors 27
28 Switch Delay Model R eq R p R n R p R p C L R n C L R p R p C int R R n R n C n L C NND2 R n Cint INV NOR2 28
29 Input Pattern Effects on Delay Delay is dependent on R R the pattern of inputs p p Low to high transition R n R n C L C int both inputs go low delay is 0.69 R p /2 C L one input goes low delay is 0.69 R p C L High to low transition both inputs go high h delay is R n C L 29
30 Delay Dependence on Input Patterns Vo oltage [V V] ==1 0 =1, =1 0 =1 0, = time [ps] Input Data Pattern Delay (psec) == =1 1, = = 0 1, =1 61 == =1, = = 1 0, =1 81 NMOS = 0.5μm/0.25 μm PMOS = 0.75μm/0.25 μm C L = 100 ff 30
31 Transistor Sizing R p R p R p R n C L 4 R p C int 2 R n Cint 1 R n R n 1 C L 31
32 Transistor Sizing a Complex CMOS Gate C 8 6 D 4 6 OUT = D + ( + C) 2 D 1 2 C 2 32
33 FanIn Considerations C D C L Distributed RC model (Elmore delay) C 3 C C 2 D t phl = 0.69 R eqn (C 1 +2C 2 +3C 3 +4C L ) C 1 Propagation delay deteriorates rapidly as a function of fanin quadratically in the worst case. 33
34 t p as a Function of FanIn t p (pse ec) t ph t p L t pl H fanin quadratic linear Gates with a fanin greater than 4 should be avoided. 34
35 t p as a Function of FanOut t p (pse ec) t p NOR2 t p NND2 t p INV eff. fanout ll gates have the same drive current. Slope is a function of driving strength 35
36 t p as a Function of FanIn and FanOut Fanin: quadratic due to increasing resistance and capacitance Fanout: each additional fanout gate adds two gate capacitances to C L t p = a 1 FI + a 2 FI 2 + a 3 FO 36
37 Fast Complex Gates: Design Technique 1 Transistor sizing i as long as fanout capacitance dominates Progressive sizing In N MN C L Distributed RC line In 3 M3 C 3 M1 > M2 > M3 > > MN (the fet closest to the output is the smallest) In 2 In 1 M2 M1 C 2 C 1 Can reduce delay by more than 20%; decreasing gains as technology shrinks 37
38 Fast Complex Gates: Design Technique 2 Transistor ordering critical path critical path charged 0 1 In 1 3 M3 C In 1 M3 C charged L L 1 In 1 In 2 M2 C 2 charged 2 M2 C 2 discharged In In 1 1 M1 C charged 3 M1 C discharged delay determined by time to discharge C L,C 1 and C 2 delay determined by time to discharge C L 38
39 Fast Complex Gates: Design Technique 3 lternative logic structures F = CDEFGH 39
40 Fast Complex Gates: Design Technique 4 Isolating fanin from fanout using buffer insertion C L C L 40
41 Fast Complex Gates: Design Technique 5 Reducing the voltage swing t phl =069(3/4(C 0.69 (C L V DD )/ I DSTn ) = 0.69 (3/4 (C L V swing )/ I DSTn ) linear reduction in delay also reduces power consumption ut the following gate is much slower! Or requires use of sense amplifiers on the receiving end to restore the signal level (memory design) 41
42 Sizing Logic Paths for Speed Frequently, input capacitance of a logic path is constrained Logic also has to drive some capacitance Example: LU load in an Intel s microprocessor is 0.5pF How do we size the LU datapath to achieve maximum speed? We have already solved this for the inverter chain can we generalize it for any type of logic? 42
43 uffer Example In Out 1 2 N C L Delay = N ( pi + gi fi ) i= 1 (in units of τ inv ) For given N: C i+1 /C i = C i /C i1 To find N: C i+1 /C i ~ 4 How to generalize this to any logic path? 43
44 Logical Effort CL Delay = k R unitcunit 1 + C γ in = τ p + g f ( ) p intrinsic delay (3kR unit C unit γ)  gate parameter f(w) g logical effort (kr unitc unit) ) gate parameter f(w) f effective fanout Normalize everything to an inverter: g inv =1, p inv = 1 Divide everything by τ inv (everything is measured in unit delays τ inv) ) ssume γ = 1. 44
45 Delay in a Logic Gate Gate delay: d = h + p effort delay intrinsic delay Effort delay: h = g f logical effort effective fanout = C out /C in Logical effort is a function of topology, independent of sizing Effective fanout (electrical effort) is a function of load/gate size 45
46 Logical Effort Inverter has the smallest logical effort and intrinsic delay of all static CMOS gates Logical effort of a gate presents the ratio of its input capacitance to the inverter capacitance when sized to deliver the same current Logical effort increases with the gate complexity 46
47 Logical Effort 47
48 Logical Effort of Gates zed delay (d) Normali g = p = d = t pnnd g = p = d = t pinv F(Fanin) Fanout (h) 48
49 Logical Effort of Gates zed delay (d) Normali g = 4/3 p = 2 d = (4/3)h+2 t pnnd t pinv g = 1 p = 1 d = h+1 F(Fanin) Fanout (h) 49
50 Logical Effort of Gates 50
51 dd ranching Effort ranching effort: b = C on path + C C off on path path 51
52 Multistage Networks Delay = N ( pi + gi fi ) i= 1 Stage effort: h i = g i f i Path electrical effort: F = C out /C in Path logical effort: G = g 1 g 2 gg N ranching effort: = b 1 b 2 b N Path effort: H = GF Path delay D = Σd i = Σp i + Σh i 52
53 Optimum Effort per Stage When each stage bears the same effort: h N = H h = N H Stage efforts: g 1 f 1 = g 2 f 2 = = g N f N Effective fanout of each stage: f = h Minimum path delay Dˆ = i g i ( ) 1/ N g f + p = NH P i i i + 53
54 Optimal Number of Stages For a given load, and given input capacitance of the first gate Find optimal number of stages and optimal sizing 1/ N D = NH + Np inv N D 1/ N 1/ ln( 1/ ( N ) N = H H + H + p = 0 inv Substitute best stage effort h = H 1/ Nˆ 54
55 Logical Effort From Sutherland, Sproull 55
56 Example: Optimize Path 56
57 Example: Optimize Path 57
58 Example: Optimize Path 1 b c a 5 g 1 = 1 g 2 = 5/3 g 3 = 5/3 g 4 = 1 Effective fanout, H = 5 G = 25/9 F = 125/9 = 13.9 f = 1.93 a = 1.93 b = fa/g 2 = 2.23 c = fb/g 3 = 5g 4 /f =
59 Example 8input ND 59
60 Method of Logical Effort Compute the path effort: F = GH Find the best number of stages N ~ log 4 F Compute the stage effort f = F 1/N Sketch the path with this number of stages Work either from either end, find sizes: C in = C out *g/f Reference: Sutherland, Sproull, Harris, Logical Effort, MorganKaufmann
61 Summary Sutherland, Sproull Harris 61
62 Ratioed Logic 62
63 Ratioed Logic V DD V DD V DD Resistive s Depletion PMOS Load Load V T < 0 Load R L In 1 In 1 In 2 PDN In 2 In 3 In 3 F PDN F In 1 In 2 In 3 V SS PDN F V SS V SS V SS (a) resistive load (b) depletion load NMOS (c) pseudonmos Goal: to reduce the number of devices over complementary CMOS 63
64 Ratioed Logic Resistive V DD N transistors + Load V OH = V DD Load OH DD R L F V OL = R PN R PN + R L In 1 In 2 In 3 PDN ssymetrical response Static power consumption V SS t pl = 0.69 R L C L 64
65 ctive Loads V DD V DD Depletion Load V T < 0 T PMOS Load F V SS F In 1 In 2 In 3 PDN In 1 In 2 In 3 PDN V SS V SS depletion load NMOS pseudonmos 65
66 PseudoNMOS V DD C D F C L V OH = V DD (similar to complementary CMOS) V 2 k V V OL k n ( DD Tn )V OL = p ( V V 2 2 DD Tp ) 2 V OL = ( V DD V T ) 1 1 k p (assuming that V k T = V Tn = V Tp ) n SMLLER RE & LOD UT STTIC POWER DISSIPTION!!! 66
67 PseudoNMOS VTC W/L p = 4 p t [V] V ou t W/L p =2 0.5 W/L p = 0.5 W/L p = 0.25 W/L p = V in [V] 67
68 Improved Loads V DD Enable M1 M2 M1 >> M2 F C D C L daptive Load 68
69 Improved Loads (2) V DD V DD M1 M2 Out Out PDN1 PDN2 V SS V SS Differential Cascode Voltage Switch Logic (DCVSL) 69
70 DCVSL Example Out Out XORNXOR gate 70
71 DCVSL Transient Response 2.5 ol ta ge [V] V ,, Time [ns] 71
72 PassTransistor Logic 72
73 PassTransistor Logic Inputs Switch Network Out Out N transistors No static consumption 73
74 Example: ND Gate 74
75 NMOSOnly Only Logic V DD In x 0.5μm/0.25μm μm/ 0.25μm 2.0 Out Voltage [V] 0.5μm/ 0.25μm 1.0 Out x In Time [ns] 75
76 NMOSonly Switch C = 2.5V C = 2.5 V = 2.5 V = 25V 2.5 M 2 M n C L M 1 V does not pull up to 2.5V, but 2.5V  V TN Threshold h voltage loss causes static power consumption NMOS has higher threshold than PMOS (body effect) 76
77 NMOS Only Logic: Level Restoring Transistor V DD Level Restorer M r V DD M 2 M n X Out M 1 dvantage: Full Swing Restorer adds capacitance, takes away pull down current at X Ratio problem 77
78 Restorer Sizing [V] Voltage W/L r =1.75/0.25 W/L r =1.50/0.25 W/L r =1.0/0.25 W/L r =1.25/0.25 Upper limit on restorer size Passtransistor pulldown can have several transistors in stack Time [ps] 78
79 Solution 2: Single Transistor Pass Gate with V T =0 V DD 0V 2.5V V DD V DD 0V Out 2.5V WTCH OUT FOR LEKGE CURRENTS 79
80 Complementary Pass Transistor Logic PassTransistor Network F (a) Inverse PassTransistor Network F F= F=+ F= ΒÝ (b) F= F=+ F= ΒÝ ND/NND OR/NOR EXOR/NEXOR 80
81 Solution 3: Transmission Gate C C C C C = 2.5 V = 2.5 V C L C = 0 V 81
82 Resistance of Transmission Gate 30 R n 2. 5 V Rn Resis stance, ohm ms R p R n R p 25V 2.5 0V R p V ou t V ou t, V 82
83 PassTransistor ased Multiplexer V DD S S S V DD M 2 S F M 1 S GND In 1 S S In 2 83
84 Transmission Gate XOR M2 M1 F M3/M4 84
85 Delay in Transmission Gate Networks In V 1 V i1 V i V i+1 V n1 V n C 0 0 C 0 C C 0 C (a) In R eq R V eq R eq R 1 V i V i+1 V eq n1 V n C C C C C m (b) In R eq R eq R eq R eq R eq R eq C C C C C C C C (c) 85
86 Delay Optimization 86
87 Transmission Gate Full dder P V DD V DD P C i C i P S Sum Generation V DD P P P V DD C o Carry Generation C i C i Setup C i P Similar delays for sum and carry 87
88 Dynamic Logic 88
89 Dynamic CMOS In static circuits at every point in time (except when switching) the output is connected to either GND or V DD via a low resistance path. fanin of n requires 2n (n Ntype + n Ptype) devices Dynamic circuits i rely on the temporary storage of signal values on the capacitance of high impedance nodes. requires on n + 2 (n+1 Ntype + 1 Ptype) transistors 89
90 Dynamic Gate Clk M p Clk M p Out Out In 1 In 2 In 3 PDN C L C Clk M e Clk M e Two phase operation Precharge (CLK = 0) Evaluate (CLK = 1) 90
91 Dynamic Gate Clk In 1 In 2 In 3 Clk M p PDN M e C L Out Two phase operation Precharge (Clk = 0) Evaluate (Clk = 1) off Clk M p on 1 Out Clk M e off on (()+C) C 91
92 Conditions on Output Once the output of a dynamic gate is discharged, it cannot be charged again until the next precharge operation. Inputs to the gate can make at most one transition during evaluation. Output can be in the high impedance state during and after evaluation (PDN off), state is stored on C L 92
93 Properties of Dynamic Gates Logic function is implemented by the PDN only number of transistors is N + 2 (versus 2N for static complementary CMOS) Full swing outputs (V OL = GND and V OH = V DD ) Nonratioed  sizing of the devices does not affect the logic levels Faster switching speeds reduced load capacitance due to lower input capacitance (C in ) reduced d load capacitance due to smaller output t loading (Cout) no I sc, so all the current provided by PDN goes into discharging C L 93
94 Properties of Dynamic Gates Overall power dissipation usually higher than static CMOS no static current path ever exists between V DD and GND (including P sc ) no glitching g higher transition probabilities extra load on Clk PDN starts to work as soon as the input signals exceed V Tn, so V M M, V IH and V IL equal to V Tn low noise margin (NM L ) Needs a precharge/evaluate clock 94
95 Issues in Dynamic Design 1: Charge Leakage CLK Clk M p Out Clk C L V Evaluate Out M e Precharge Leakage sources Dominant component is subthreshold current 95
96 Solution to Charge Leakage Keeper Clk M p M kp C L Out Clk M e Same approach as level restorer for passtransistor logic 96
97 Issues in Dynamic Design 2: Charge Sharing Clk M p C L Out Charge stored originally on C L is redistributed (shared) over C L and C leading to reduced robustness =0 Clk M e C C 97
98 Charge Sharing Example Clk Out C L =50fF C a =15fF! C b =15fF C c =15fF C C C d =10fF Clk 98
99 Charge Sharing V DD case 1) if ΔVV out < V Tn Clk M p M a X Out C L C V = L DD C V t + C V V V L out ( ) a ( DD Tn ( X ) ) or ΔV out = V out ( t) V DD = C a V ( C DD V Tn ( V X )) L = 0 M b C a case 2) if ΔV out > V Tn Clk M e C b C a ΔV out V = DD C a + C L 99
100 Solution to Charge Redistribution Clk M p M kp Clk Out Clk M e Precharge internal nodes using a clockdriven transistor (at the cost of increased area and power) 100
101 Issues in Dynamic Design 3: ackgate Coupling Clk M p Out1 =1 Out2 =0 C L1 C L2 =0 =0 In Clk M e Dynamic NND Static NND 101
102 ackgate Coupling Effect Clk Out1 0 In Out Time, ns 102
103 Issues in Dynamic Design 4: Clock Feedthrough h Clk Coupling between Out and M p Clk input of the precharge Out device due to the gate to C L drain capacitance. So voltage of Out can rise above V DD. The fast rising Clk M e (and falling edges) of the clock couple to Out. 103
104 Clock Feedthrough Clk Out 2.5 Clock feedthrough In 1 In In 3 In In & Clk Out Clk Time, ns Clock feedthrough 104
105 Other Effects Capacitive coupling Substrate coupling Minority charge injection Supply noise (ground bounce) 105
106 Cascading Dynamic Gates V Clk Clk M p M p In Out1 Out2 Clk In Clk M e Clk M e Out1 V Tn Out2 ΔV t Only 0 1 transitions allowed at inputs! 106
107 Domino Logic Clk M p Out1 Clk M p In 1 In 2 PDN In 4 PDN In In 3 5 Clk M e Clk M e M kp Out2 107
108 Why Domino? Clk In i In j Clk PDN In i PDN In i PDN In i PDN In j In j In j Like falling dominos! 108
109 Properties of Domino Logic Only noninverting logic can be implemented Very high speed static inverter can be skewed, only LH transition Input capacitance reduced smaller logical effort 109
110 Designing with Domino Logic V DD V DD V DD Clk M p Out1 Clk M p M r Out2 In 1 In 2 PDN In 4 PDN In 3 Can be eliminated! Clk M e Clk M e Inputs = 0 during gprecharge 110
111 Footless Domino 111
112 Differential (Dual Rail) Domino Out = off on Clk M kp Clk M p M kp !! M p Out = Clk M e Solves the problem of noninverting logic 112
113 npcmos Clk M p Out1 Clk In In 1 4 PUN In 2 PDN In In 3 Out2 0 1 (to PDN) Clk Clk M p M e M e Only 0 1 transitions allowed at inputs of PDN Only 1 0 transitions allowed at inputs of PUN 113
114 NOR Logic Clk In 1 In 2 M p PDN Clk Out1 In 4 In M e PUN In 5 In 3 Clk Clk M M e M p Out2 (to PDN) to other PDN s to other PUN s WRNING: Very sensitive to noise! 114
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